RU-ALLRUSSIAN 1981 Problem 5

Let S be the set of points (x, y) given by $\mathrm{y}\leq - \mathrm{x}^2$ and $\mathrm{y}\geq \mathrm{x}^2 - 2\mathrm{x} + \mathrm{a}$ . Find the area of the rectangle with sides parallel to the axes and the smallest possible area which encloses S.